A fully automatic computerized method for segmenting contours of corneal endothelial cells is proposed. As part of the method, scale-space filtering (i.e. Gaussian filtering) is used to achieve tasks different from noise removal. This type of filtering is applied making use of the separability property of Gaussian kernels, avoiding the erosion of images. A variant of unsharp masking is used to considerably increase the visibility of dark areas of images. It is shown how the overflow that occurs when two images are subtracted can be handled to produce better results than normal unsharp masking. The method is exemplified with a low quality specular micrograph. To test the performance of the method, its output is used to automatically calculate the average cell size of images of different samples of tissue and different visual quality. The obtained results are successfully compared to those obtained with a manual semi-automatic method. A method for reading the segmented contours is suggested as well as two shape representations to achieve morphometric analysis of individual cells.